Plato's most enduring influence on science was his advice to approach the study of nature as an exercise in geometry. Through this "geometrization of nature," which could best be done in disciplines that could be suitably idealized, such as astronomy, one can formulate laws that are as "certain" as those in geometry. As Plato has Socrates remark in the Republic : "Let's study astronomy by means of problems, as we do in geometry, and leave the things in the sky alone."
It has been a long road from Plato's Meno to the present, but it is perhaps encouraging that most of the progress along that road has been made since the turn of the twentieth century, and a large fraction of it since the midpoint of the century. Thought was still wholly intangible and ineffable until modern formal logic interpreted it as the manipulation of formal tokens. And it seemed still to inhabit mainly the heaven of Platonic ideals, or the equally obscure spaces of the human mind, until computers taught us how symbols could be processed by machines.allen newell
But progress in knowledge has made us aware of the superficiality of Plato's lumping of individuals and their original powers into a few sharply marked-off classes; it has taught us that original capacities are indefinitely numerous and variable. It is but the other side of this fact to say that in the degree in which society has become democratic, social organization means utilization of the specific and variable qualities of individuals, not stratification by classes.john dewey
These ideas are present in all sorts of unrelated cultures -- the Easter Islands, Celtic mythology, Plato's Symposium with its notion that we are all originally hermaphrodite. We became too arrogant and so the gods split us down the middle, forcing us to spend our lives chasing our other half. If we start being arrogant all over again, God will come down and split each half in half, and it will take four people to assemble a fifth, making our lives peculiarly, desperately difficult.Peter Greenaway
Do what nature now requires. Set thyself in motion, if it is in thy power, and do not look about thee to see if any one will observe it; nor yet expect Plato's Republic: but be content if the smallest thing goes on well, and consider such an event to be no small matter.marcus aurelius
See there the olive grove of Academe, Plato's retirement, where the Attic bird Trills her thick-warbled notes the summer long.john milton
Mystical doctrines as to the relation of time to eternity are also reinforced by pure mathematics, for the mathematical objects, such as numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God's thoughts. Hence Plato's doctrine that God is a geometer, and Sir James Jeans' belief that He is addicted to arithmetic.
[ Aristotle ] totally misrepresents Plato's doctrine of "Ideas." ...It is also pertinent to inquire, what is the difference between the "formal cause" of Aristotle and the archetypal ideas of Plato? ... Yet Aristotle is forever congratulating himself that he alone has properly treated the "formal" and the "final cause"!
To his [ Plato's ] great disappointment, he found Anaxagoras adducing simple physical reasons, instead of the teleological reasons, which he had expected. Such a teacher could no longer allure him.george henry lewes
With regard to this question modern physics takes a definite stand against the materialism of Democritus and for Plato and the Pythagoreans . The elementary particles are certainly not eternal and indestructible units of matter, they can actually be transformed into each other. ... The elementary particles in Plato's Timaeus are finally not substance but mathematical forms.werner heisenberg
Plato's discovery went as follows. It is possible for something to be a certain way and for something else to be the same way. So There are universals. (Tumultuous applause, which lasts, despite occasional subsidences, 2,400 years.)[…] ' Universals ' is simply the name philosophers give to the ways in which two or more things can be the same.
Plato complete works, annotated and searchable, at ELPENOR Euthyphro LibriVox recording Ion LibriVox recording Quick Links to Plato's Dialogues (English, Greek, French, Spanish)
Do what nature now requires. Set thyself in motion, if it is in thy power, and do not look about thee to see if any one will observe it; nor yet expect Plato's Republic: but be content if the smallest thing goes on well, and consider such an event to be no small matter.